WITHDRAWN: Parallel Block Coordinate Descent with Path-Following for Constrained Folded Concave Linear Regression

Abstract

Abstract This paper focuses on solving folded concave penalized linear regression with inequality constraints, which is one of the typical optimization problems of minimizing the sum of a smooth (possibly nonconvex nonlinear) function and a block-separable nonconvex nonsmooth function involving a large number of block variables subject to inequality constraints. Recent theoretical analysis has demonstrated the superiority of the solution of this problem over those obtained from its convex counterparts in statistics. However, solving such a large-scale nonconvex nonsmooth optimization problem associated with inequality constraints remains a big challenge. To this end, we propose a new parallel first-order optimization method, noted as Parallel Block Coordinate Descent with Path-Following (PBCD-PF), which combines the classical path-following method and the recent popular block coordinate descent method in a shared memory system. Experiments conducted on constrained folded concave penalized linear regression and the parallel experiment results of the proposed algorithm validate the proposed algorithm's efficacy as well as scalability.